Compact schemes which function as finite difference methods are preferred for the higher accuracy they impart to the solutions. These schemes use implicit stencils to compute derivatives with `near-spectral 'resolution while using relatively coarser grids. Most compact schemes for partial differential equations (PDEs) originate from the Padé discretization schemes for ordinary differential equations (ODEs). There are many compact schemes [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} developed for PDEs, among many others. It has been shown in [9]} that analyzing spatial resolution alone is insufficient for solving space-time dependent PDEs while using an alternative to the von Neumann method [10]} for quantifying numerical stability. Using the global spectral analysis (GSA) developed for space-time dependent problems, the necessary condition for accuracy is that the scheme must preserve the physical dispersion relation obtained from the governing equation and boundary conditions. This is equivalent to stating that for a model 1D convection equation, the numerical group velocity must match with the corresponding physical group velocity for a large range of wavenumbers, as the energy propagates with this parameter [11]}, [12]}. Numerical methods satisfying such criteria are referred to as dispersion relation preserving (DRP) schemes [2]}, [14]}. Recently, this concept has been used to develop a novel compact scheme in a parallel framework [15]} which removes errors due to parallelization using GSA. The added motivation of developing an analysis that did not only comment on the numerical stability of a method [10]}, [17]}, [18]} was based on the observation that the solution must propagate at the correct speed with attenuation and dispersion as described by the governing equation. This was found to be all the more important in numerical weather prediction [19]}, where the correct propagation of disturbances is vital. The need for developing GSA has also been discussed in [2]}, [6]}, [22]}.
